Computer Algebra System (CAS) for Scala

Question

I am looking for a simple CAS system for scala.

It should have the following functions:

• provide access to an abstract syntax tree (preferably using case classes for easy matching)
• divided Stringby AST
• simplify expressions

---

If nothing exists, and I have to write something basic, a better idea?

I think something like this:

abstract trait Term
{
  def simplify:Term
  def evaluate(assignment:Var => Double):Double
  def derivative:Term
}

case class Const(c:Int) extends Term
case class Var(x:String) extends Term

case class Negate(x:Term) extends Term
case class Subtract(x:Term, y:Term) extends Term
case class Divide(x:Term, y:Term) extends Term


object Add { def apply(x:Term*):Add = Add(x.toList) }
case class Add(xs : List[Term]) extends Term

object Multiply { def apply(x:Term*):Multiply = Multiply(x.toList) }
case class Multiply(xs:List[Term]) extends Term

case class Power(x:Term, y:Term) extends Term
case class Exp(x:Term) extends Term

I would follow the simplification algorithm described here , which seems tedious. (But maybe boredom is inevitable when it comes to simplifying algebraic expressions?)

Some criticisms of this particular implementation:

• I will recursively call simplifycase classes all over the place of arguments (it seems that it can be somehow centralized)
• varargs/ List Add Mutliply ,

Answer 1

CAS Scala.

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sealed trait Term
case class Const(c : Double) extends Term
case class Var(x : String) extends Term
case class Negate(x : Term) extends Term
case class Multiply(xs : List[Term]) extends Term
// etc

object CAS {

  // I assume that the assignment map may be incomplete, thus
  // evaluation is really a partial substitution and then simplification
  def evaluate(t : Term, assignment : Var => Option[Double]) : Term = t match {
    case _ : Const => t
    case v : Var => assignment(v) map Const getOrElse v
    case Negate(x) => evaluate(Multiply(Const(-1) :: evaluate(x, assignment) :: Nil), assignment)
    case Multiply(ts) => {
      val evalTs = ts map { t => evaluate(t, assignment) }
      val flattened = evalTs flatMap {
         case Multiply(subs) => subs
         case t => List(t)
      }
      val constTotal = Const((flattened collect { case Const(c) => c }).product)
      val otherTerms = flattened filter { case t : Const => false; case _ => true }
      (constTotal, otherTerms) match {
         case (Const(0), _) => Const(0)
         case (Const(1), Nil) => Const(1)
         case (Const(1), _) => Multiply(otherTerms)
         case _ => Multiply(constTotal +: otherTerms)
      }
    }
    // etc

  }

  private val emptyAssignment : (Var => Option[Double]) = { x : Var => None }

  // simplfication is just evaluation with an empty assignment
  def simplify(t : Term) : Term = evaluate(t, emptyAssignment)
}

, , . . . Kiama http://code.google.com/p/kiama/ Scala

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